An example will elucidate the whole process. In August 1775, General Roy observed the barometer on Caernarvon Quay at 30.091 inches, the attached thermometer being 15°.7, and the detached 15°.6 centigrade, while on the Peak of Snowdon the barometer stood at 26.409, the attached thermometer marking 10°.0, and the detached 8°.8. Here, twice the difference of the attached thermometers is 11°.4, which multiplied into .00264 gives .030, for the correction of the upper barometer. Next, 30.091 + 26.439: 30.091 + 26.439, or 56.530 : 3.652 :: 52000: 3359. Again, twice the sum of the degrees marked on the detached thermometers is 48.8, which multiplied into 3.359 gives 164; wherefore, the true height of Snowdon above the Quay of Caernarvon is 3359+164, or 3533 feet. The correction for centrifugal force is only 7 feet more. This mode of approximation may be deemed sufficiently near, for any heights which occur in this island; but greater accuracy is attained by assuming intermediate measures. To illustrate this, I shall select another example. At the very period when General Roy was making his barometrical observations at home, Sir George Shuckburgh Evelyn found the barometer to stand at 24.167 on the summit of the Mole, an insulated mountain near Geneva, the attached and detached thermometers indicating 14°.4 and 13°.4, while they marked 16°.3 and 17°.4 at a cabin below and only 672 feet above the lake, the altitude of the barometer at this station being 28.132. Now, 3.8x .0024.009, and 24.167+009 24.176; the arithmetical mean between which and 28.132 is 26.154; and hence, separately, 50.330: 1.978: : 52000: 2044, and 54.286: 1.978 :: 52000: 1895. Wherefore, joining these two parts, 2044+ 1895, or 3939 expresses the approximate height. The final correction is 61.6x 3.939=243, or 254 feet, if allowance be made for the effect of centrifugal force, and consequently the Mole has its summit elevated 4865 feet above the lake of Geneva, and 6063 above the level of the sea.

In general, let A and A+ nb denote the correct lengths of the columns of mercury at the upper and the lower stations; the approximate height of the mountain will be expressed by

If n were assumed a large number, the result would approach to the accuracy of a logarithmic computation, though such an extreme degree of precision will be scarcely ever wanted.

To expedite the calculation of heights from barometrical observations, I have now caused Mr Cary, optician in London, to make for sale a sliding-rule, of an easy and commodious construction. That small instrument, which should be accompanied with a barometer of the lightest and most portable kind, will be found very useful to mineralogical travellers who have occasion to explore mountainous tracts. Nothing could tend more to correct our ideas of physical geography, than to have the principal heights in all countries measured, at least with some tolerable degree of precision. But the elevation of any place above the sea may be ascertained very nearly, from the comparison of even very distant barometrical observations, especially during the steadiness of the fine season in the happier climates. In the summer of 1814, Engelhardt and Parrot, two Prussian travellers, by a series of fifty-one barometrical observations, made along the distance of 711 miles, from the Caspian to the Black Sea, ascertained the former to be 334 English feet below the level of the latter, which completely oversets the supposition of any subterranean communication existing between those seas. By the same mode may be traced a profile or vertical section, that shall exhibit at one glance the great features of a country. As a specimen, I have combined and reduced the sections which the celebrated philosophic traveller Humboldt has given of the continent of America, running in a twisted direction from Acapulco to Vera Cruz, and connecting the Pacific with the Atlantic Ocean.

A ACAPULCO.

a Peregrino.

B CHILPANSINGO, b Mescala.

c Tepecuacuilco.

d Puente de Istla.

C CUERNAVACA.

e La Cruz del Marques. D MEXICO.

f Venta de Chalco.

g St Martin.

E LA PUEBLA DE LOS ANGELES.

h El Pinal.

i Perote.

k Cruz Blanca.

F XALAPA.

G VERA CRUZ.

702000

5000

10'000

5000

A a B b c Fd Ce Df g Ehik G

The divided scale expresses the horizontal distance in miles, while the parallels, on a much larger scale, mark the elevation. in feet. This profile is really composed of four successive sections, which are distinguished by opposite shadings. The survey proceeded first along the road from Acapulco to Mexico, thence to Puebla de los Angeles, next to Cruz Blanca, and finally to Vera Cruz. These several directions and distances are expressed in the ground plan.

An attempt is likewise made in this profile, to convey some · idea of the geological structure of the external crust: Limestone is represented by straight lines slightly inclined from the horizontal position.

Basalt, by straight lines slightly reclined from the perpendicular.

Porphyry, by waved lines somewhat reclined.

Granite, by confused hatches.

Amygdaloid, by confused points.

But the easiest way of estimating within moderate limits the elevation of a country, is founded on the difference between the standard and the actual mean temperature as indicated by deep wells or copious and shaded springs. Professor Mayer

of Göttingen, from a comparison of distant observations on the surface of the globe, proposed a formula, which, with a slight modification, appears to exhibit correctly the temperature of any place at the level of the sea. Leto denote the latitude; and 29 cosq',

or 144 suvers 20, will express, in degrees of the centigrade scale, the medium heat on the coast. But the gradations of climate are more easily conceived by help of a geometrical diagram. From the centre C, draw straight lines to the several degrees of the quadrant, and cutting the interior semi

circle; then the radius CA denoting 29°, the perpendiculars from the points of section will intercept segments proportional to the mean temperature expressed on DE.

The higher regions are invariably colder than the plains; and I have been able, after a delicate and patient research, to fix the law which connects the decrease of temperature with the altitude. If B and b denote the barometric pressure at the lower and upper stations; then will (

B

b

b

B

25 express,

on the centigrade scale, the diminution of heat in ascent. Hence, for any given latitude, that precise point of elevation

b

may be found, at which eternal frost prevails. Put x=B

and the standard temperature; then (—=— x ) 25=t, or

x2+ .04 tx = 1, which quadratic equation being resolved, gives the relative elasticity of the air at the limit of congelation, whence the corresponding height is determined. From these data the following table has been calculated.